Suppose $F$ is a field of characteristic $p\neq 0$ and $H$ is a $p$-primary abelian $A$-group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$.
@article{118507,
author = {William Ullery},
title = {A direct factor theorem for commutative group algebras},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {33},
year = {1992},
pages = {383-387},
zbl = {0794.16022},
mrnumber = {1209281},
language = {en},
url = {http://dml.mathdoc.fr/item/118507}
}
Ullery, William. A direct factor theorem for commutative group algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 383-387. http://gdmltest.u-ga.fr/item/118507/
Infinite Abelian Groups, Volumes I and II, Academic Press, New York, 1970 and 1973. | Zbl 0338.20063
The classification of $N$-groups, Houston J. Math. 10 (1984), 43-55. (1984) | MR 0736574 | Zbl 0545.20042
On the structure of abelian $p$-groups, Trans. Amer. Math. Soc. 288 (1985), 505-525. (1985) | MR 0776390 | Zbl 0573.20053
A note on a theorem of May concerning commutative group algebras, Proc. Amer. Math. Soc. 110 (1990), 59-63. (1990) | MR 1039530 | Zbl 0704.20007
Modular group algebras of totally projective $p$-primary groups, Proc. Amer. Math. Soc. 76 (1979), 31-34. (1979) | MR 0534384 | Zbl 0388.20041
Modular group algebras of simply presented abelian groups, Proc. Amer. Math. Soc. 104 (1988), 403-409. (1988) | MR 0962805 | Zbl 0691.20008
Ulm invariants of Sylow $p$-subgroups of group algebras of abelian groups over fields of characteristic $p$, Pliska 2 (1981), 77-82. (1981) | MR 0633857
An isomorphism theorem for commutative modular group algebras, Proc. Amer. Math. Soc. 110 (1990), 287-292. (1990) | MR 1031452 | Zbl 0712.20036
A classification theorem for abelian $p$-groups, Trans. Amer. Math. Soc. 210 (1975), 149-168. (1975) | MR 0372071 | Zbl 0324.20058